1. Field of the Invention
The invention is related to the field of well log data processing. More specifically, the invention is related to methods of inversion processing of well log data to derive a parametric model of earth formations which would produce a well log instrument response similar to well log data actually measured within a wellbore drilled through the earth formations.
2. Description of the Related Art
Well logging instruments make measurements related to various physical properties of earth formations from within wellbores drilled through these earth formations. The physical properties can include, among other things, electrical resistivity, and acoustic propagation velocity in one or more modes of acoustic energy propagation. The actual values of the measurements made by the well logging instruments depend not only on the values of these physical parameters but also on the spatial distribution of the response of each well logging instrument. Consequently, the spatial distribution of earth formations having the particular values of the physical parameters also affects the measurements made by the well logging instruments.
A process known in the art for determining both the spatial distribution and the values of the physical properties of the earth formations is called inversion processing. Inversion processing is described, for example, in D. L. B. Jupp and K. Vozoff, Stable Iterative Methods for Geophysical Inversion, Geophysical Journal of the Royal Astronomical Society, vol. 42, pp. 957-976 (1975). Inversion processing is usually performed by generating an initial estimate, or model, of the values and of the spatial distribution of the physical properties of the earth formations through which the wellbore is drilled. Since the spatial distribution is generally known for the response of the particular logging instruments for which the inversion process is being performed, a synthetic set of instrument responses, or synthetic well log, can be generated from the initial model. If the initial model does not precisely represent the actual distribution of physical properties of the formations through which the wellbore is drilled, there will generally be some differences between the measured well log data and the synthetic well log. If there are significant differences between the synthetic well log and the measured well log, the initial model will be "adjusted", meaning that the spatial distribution and/or the values of the physical properties will be changed, and a new synthetic well log will be generated from the adjusted initial model. If the differences between the synthetic well log made from the adjusted model, and the measured log data are still significant, the steps of adjusting the model, generating the synthetic well log and comparing the newest synthetic well log to the measured well log are repeated until the differences between the synthetic and the measured well logs are minimized. The model as finally adjusted is then deemed to be a reasonable representation of the spatial distribution and the values of the physical properties of the earth formations.
As initially described by jupp and Vozoff, supra, inversion was "one-dimensional", meaning that the spatial distribution of the physical properties was deemed to be variable only along the axis of the wellbore. The earth formations did not change properties radially outward from the wellbore. Later advances in inversion processing enabled determining a spatial distribution of physical properties in both the axial and radial directions, this being so-called "two-dimensional" inversion.
A limitation to the inversion processing known in the art is that it is generally performed only for a single type of well log measurement. In certain instances, inversion processing data from different types of well logging instruments measuring the same earth formations may each result in a different finally adjusted model (wherein the differences between the synthetic well log and the measured well log are minimized). Differences between finally adjusted models for each type of well log instrument make it difficult to resolve the most likely spatial distribution of properties of the earth formations through which the wellbore is drilled.
One method to improve inversion processing is described in A. G. Mezzatesta et al, Improved Resolution of Reservoir Parameters by Joint Use of Resistivity and Induction Tools, Society of Professional Well Log Analysts, Houston, Tex., (1994). The method described in the Mezzatesta et al reference includes generating a single earth model which minimizes the differences between synthetic and measured well log data for a combination of galvanic and induction type electrical resistivity measurements run in the same wellbore (and consequently through the same earth formations). A drawback to the use of the method described in the Mezzatesta et al reference is that wellbore operators typically do not run both galvanic and induction type resistivity well logging instruments in the same wellbore for reasons of cost and operating efficiency. Further, wellbore conditions and earth formation resistivity values which are more suitably logged with induction well logging instruments can be undesirable for logging with typical galvanic well logging instruments, and vice versa. Consequently, the method described by Mezzatesta et al has not yet found wide commercial application.
Other types of well logging instruments are more commonly used in combination with either galvanic or induction well logging instruments, but as yet no inversion processing has been devised to make use of the various types of well log data available from the typical wellbore, primarily because the different well logging instruments measure fundamentally different physical properties of the earth formations. Accordingly, the invention is intended to provide a method of jointly inversion processing resistivity and acoustic well log data.